Answer:
electromagnetic waves only
Explanation:
I just took the test, Hope it helps!
Answer:
A: Electromagnetic waves only
Explanation:
PLEASE HELP and actually help plz
The position of masses 4kg, 6kg, 7kg, 10kg ,and 3kg are (0,1), (4,2), (3,5), (5,6), and (-2,4) respectively. Where must you place a mass of 13kg if you want the center of mass to be at (-1,-3)?
Answer:
iEvaluate for \(x=2.\)Evaluate for \(x=2.\)Evaluate for \(x=2.\)Evaluate for \(x=2.\)Evaluate for \(x=2.\)Evaluate for \(x=2.\)Evaluate for \(x=2.\)
Explanation:
Vector A is 3 units length and points along the positive x-axis vector B is 4 units in length and points along negative y-axis .find magnitude and direction of the vector (a) A+B (b)A-B
Answer:
a) < 3 , -4 >
b) < 3 , -4 >
Explanation:
a) If you can imagine this, adding vectors is like putting them "tip to tail", where you put the beginning point of vector B to the end point of vector A (or vice versa). Your new vector (A+B) would be from the "tip" of vector A to the "tail" of vector B.
Mathematically, this is the same as adding the x-components of each vector together as well as the y-components.
Vector A: 3 units along the positive x-axis: < 3 , 0 >
Vector B: 4 units along the negative y-axis: < 0 , -4 >
A+B = < 3 , 0 > + < 0 , -4 > = < (3+0) , (0+(-4)) > = < 3 , -4 >
b) Subtracting is like adding a negative, so you could use the same "tip to tail" visual by adding the negative of vector B instead (which is B in the opposite direction).
Vector A: < 3 , 0 >
Vector B: < 0 , -4 >
Vector -B: < 0 , 4 >
A-B = A+(-B) = < 3 , 0 > + < 0 , 4 > = < (3+0) , (0+4) > = < 3 , 4 >
Two resistors are connected in parallel. If R1 and R2 represent the resistance in Ohms (Ω) of each resistor, then the total resistance R is given by 1R=1R1+1R2. Suppose that in fact, these two resistors are actually potentiometers (resistors with variable resistance) and R1 is increasing at a rate of 0.4Ω/min and R2 is increasing at a rate of 0.6Ω/min. At what rate is R changing when R1=117Ω and R2=112Ω?
Answer:
1/Re= 1/R1 + 1/R2
Explanation:
Two resistors are connected in parallel. If R1 and R2 represent the resistance in Ohms (Ω) of each resistor, then the total resistance R is given by [tex]\mathbf{\dfrac{1}{R}=\dfrac{1}{R_1}+\dfrac{1}{R_2}}[/tex]. Thus, the rate of R changes when R₁ = 117 Ω and
R₂ = 112 Ω is 0.25 Ω/min
For a given resistor connected in parallel;
[tex]\mathbf{\dfrac{1}{R}=\dfrac{1}{R_1}+\dfrac{1}{R_2}}[/tex]
Making R from the left-hand side the subject of the formula, then:
[tex]\mathbf{R = \dfrac{R_1R_2}{R_1+R_2}}[/tex]
Given that:
[tex]\mathbf{R_1 = 117,}[/tex] [tex]\mathbf{R_2 = 112 }[/tex]Now, replacing the values in the above previous equation, we have:
[tex]\mathbf{R = \dfrac{13104}{229}}[/tex]
However, the differentiation of R with respect to time t will give us the rate at which R is changing when R1=117Ω and R2=112Ω.
So, by differentiating the given equation of the resistor in parallel with respect to time t;
[tex]\mathbf{\dfrac{1}{R}=\dfrac{1}{R_1}+\dfrac{1}{R_2}}[/tex], we have:
[tex]\mathbf{\dfrac{1}{R^2}(\dfrac{dR}{dt})=\dfrac{1}{R_1^2}(\dfrac{dR_1}{dt})+\dfrac{1}{R_2^2}(\dfrac{dR_2}{dt})}[/tex]
[tex]\mathbf{(\dfrac{dR}{dt})=R^2 \Bigg[ \dfrac{1}{R_1^2}(\dfrac{dR_1}{dt})+\dfrac{1}{R_2^2}(\dfrac{dR_2}{dt})\Bigg]}[/tex]
[tex]\mathbf{\dfrac{dR}{dt}=(\dfrac{13104}{229})^2 \Bigg[ \dfrac{0.4}{117^2}+\dfrac{0.6}{112^2}\Bigg]}[/tex]
[tex]\mathbf{\dfrac{dR}{dt}=3274.44 \Bigg[ (7.7052 \times 10^{-5} )\Bigg]}[/tex]
[tex]\mathbf{\dfrac{dR}{dt}=0.25\ \Omega /min}[/tex]
Therefore, we can conclude that the rate at which R is changing R1=117Ω and R2=112Ω is 0.25 Ω/min
Learn more about resistors here:
https://brainly.com/question/17390255?referrer=searchResults
What is the power generated by a motor boat that applies a 1500 N force over 1000 m in 60 seconds?
Why must you bend forward when carrying a
heavy load on your back?
1. The gravitational force has decreased.
2. Angular momentum has decreased.
3. The center of gravity has shifted.
4. Inertia has changed.
Answer:
hi I thinks its number 3
Explanation:
hope you have a nice day
What is the difference between a positively and negatively charged object?
Answer:
Positively charged objects have electrons; they simply possess more protons than electrons. Negatively charged objects have protons; it's just their number of electrons is greater than their number of protons.
The difference between a positively charged object and a negatively charged object is the number of protons and electrons. The imbalance in charge results into formation of charged objects.
What are Charged objects?
Charged objects have an imbalance of charge that is either more negative electrons than the positive protons or more positive protons than the negative electrons in the object. The neutral objects are those species which have a balance of charge with equal number of protons and electrons.
A positively charged object is formed when an atom has more protons than electrons. And, a negatively charged object is formed when an atom has more electrons than protons. As, electrons have a negative charge and protons have a positive charge.
Learn more about Charged objects here:
https://brainly.com/question/535279
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Consider a pulley of mass mp and radius R that has a moment of inertia 1/2mpR2. The pulley is free to rotate about a frictionless pivot at its center. A massless string is wound around the pulley and the other end of the rope is attached to a block of mass m that is initially held at rest on frictionless inclined plane that is inclined at an angle β with respect to the horizontal. The downward acceleration of gravity is g. The block is released from rest .
How long does it take the block to move a distance d down the inclined plane?
Write your answer using some or all of the following: R, m, g, d, mp,
Answer:
a = [tex]\frac{m}{m+ \frac{1}{2} m_p} \ g \ sin \beta[/tex] , t = [tex]\sqrt{ \frac{2d}{a} }[/tex]
Explanation:
To solve this exercise we must use Newton's second law
For the block
let's set a reference system with the x axis parallel to the plane
X axis
Wₓ - T = m a
Y axis
N- W_y = 0
N = W_y
for pulley
∑τ = I α
T R = (½ m_p R²) α
let's use trigonometry for the weight components
sin β = Wₓ / W
cos β = W_y / W
Wx = W sin β
angular and linear variables are related
a = α R
α = a / R
we substitute and group our equations
W sin β - T = m a
T R = ½ m_p R² (a / R)
W sin β - T = m a
T = ½ m_p a
we solve the system of equations
W sin β = (m + ½ m_p) a
a = [tex]\frac{m}{m+ \frac{1}{2} m_p} \ g \ sin \beta[/tex]
let's find the time to travel the distance (d) through the block
x = v₀ t + ½ a t²
d = 0 + ½ a t²
t = [tex]\sqrt{ \frac{2d}{a} }[/tex]
Which one of the following statements is not true of free falling object
Answer:
FORCE as for my answer....
a student starts his lawnmower by applying a constant tangential force of 150 N to the 0.3 kg disk-shaped flywheel. the radius of the flywheel is 18 cm. what is the flywheels angular acceleration? b. what is the angular speed of the wheel after it has turned through one revolution,( neglect friction and motor compression.) c. what is the tangent speed of a point on the rim of the flywheel?
Answer:
okay
Explanation:
please I don't know
Which one of the following
statements about electric
current is correct?
- Current is calculated as the amount of charge that pass
a point on a circuit per time.
- Current is calculated as the amount of resistance a
charge encounters in a given time.
- Current is calculated as the amount of energy a charge
loses per unit of time.
- Current is calculated as the distance that a charge
moves per unit of time
Answer:
Current is calculated as the amount of charge that pass a point on a circuit per time.
Explanation:
Electric current is defined as the amount of charge that passes a point on a circuit per unit time. The mathematical definition of electric current is given by :
[tex]I=\dfrac{q}{t}[/tex]
Where
q is a charge (Coulomb)
t is time (in seconds)
The SI unit of electric current is A. It is equivalent to C/s. So, the correct option is (A).
I WILL REPORT YOU IF YOU DON'T ANSWER QUESTION OR IF YOU PUT A LINK
Which of the following statements are true
A simple generator is used to generate a peak output voltage of 23.0 V . The square armature consists of windings that are 5.1 cm on a side and rotates in a field of 0.500 T at a rate of 55.0 rev/s .
How many loops of wire should be wound on the square armature?
Answer: 51
Explanation:
Given
Output is 23 V
The square armature side is [tex]a=5.1\ cm[/tex]
Magnetic field [tex]B=0.5\T[/tex]
Rate of revolution [tex]n=55\ rev/s[/tex]
Angular speed
[tex]\omega =2\pi n\\\omega=2\pi \times 55=110\pi\ rad/s[/tex]
Peak voltage is given by
[tex]E_{peak}=NB\omega A\quad [\text{N=Number of windings; A=area of cross-section}]\\\\N=\dfrac{E_{peak}}{B\omega A}\\\\N=\dfrac{23}{0.5\times 110\pi\times (0.051)^2}\approx 51[/tex]
So, there are approximate 51 loops
An amusement park ride swings back and forth once every 60.0 s. What is the ride's frequency?
The Answer choices are in the image above
Answer:
Option B. 0.016 Hz
Explanation:
From the question given above, the following data were obtained.
Period (T) = 60 s
Frequency (f) =?
Frequency and period are related according to the following equation:
Frequency = 1 / period
f = 1/T
With the above formula, we can obtain the frequency of the ride as follow:
Period (T) = 60 s
Frequency (f) =?
f = 1/T
f = 1/60
f = 0.016 Hz
Thus, the rider's frequency is 0.016 Hz
What is the height of a copper cylinder ( ρCu = 8.96 gcm-3) of diameter 10 cm with a mass of 10 kg ?
Answer:
h=0.142m=14.2cm
Explanation:
ρ=8.96 g/cm3=8960 kg/m3
d=0.1m
ρ=m/V - - >ρ=m/[π*((d/2)^2) *h] - - >
8960=10/[π*((0.1)^2) *h] - - >
h=0.142m
Astronomers define the __________ as all of space and everything in it. It is enormous, almost beyond imagination. Question 2 options: galaxy none of these universe solar system
Answer:
Universe
Explanation:
I took the quiz.
A uniform electric field is present in the region between infinite parallel plane plates A and B and a uniform electric field is present in the region between infinite parallel plane plates B and C. When the plates are vertical, is directed to the right and to the left. The signs of the charges on plates A, B and C may be:_______.
A. -- ,--, --
B. + , -- , --
C. + , --, +
Answer:
the correct answer is C +, - , +
Explanation:
The electric field for positive charges is outgoing and for negative charges it is directed towards the charge.
Let's apply this to our case:
On plates A and B the field goes to the right, therefore plate A must be positive
In plates B and C the way it goes to the left, so the field is selected from it, this implies that plate C is positive
therefore plate B must be negative for both cases
when checking the correct answer is C +, - , +
A proton (with charge of 1.6 x 10^-19 C and mass of 1.7*10^-27 kg) traveling at a speed of 57,600,630 m/s in the + x-direction enters a region of space where there is a magnetic field of strength 0.5 T in the - z-direction. What would be the radius of the circular motion that the proton would go into if it is "trapped" in this magnetic field region?
Answer:
r = 1,224 10⁻² m
Explanation:
For this exercise let's use Newton's second law
F = m a
the force is magnetic
F = q v x B
The bold letters indicate vectors, the module of this expesion is
F = q v B
The direction of the force is found by the right hand rule
thumb points in the direction of the velicad + x
fingers extended in the direction of B -z
the palm is in the direction of the force + and
the acceleration of the proton is cenripetal
a = v² / r
we substitute
q v B = m v² / r
r = [tex]\frac{m \ v}{q \ B}[/tex]
let's calculate
r = [tex]\frac{1.7 \ 10^{-27} \ 5.760063 \ 10^7 }{1.6 \ 10^{-19} \ 0.5 }[/tex]
r = 1,224 10⁻² m
a disk of a radius 50 cm rotates at a constant rate of 100 rpm. what distance in meters will a point on the outside rim travel during 30 seconds of rotation?
Distance travelled in one round will be equal to the circumference of the disc i.e [tex] 2 \pi r[/tex]
Radius=50cm
Circumference= [tex] 2 \times \frac{22}{7} \times 50cm=> \frac{2200}{7} cm[/tex]
If the disc rotates at speed of 100rpm that means it completes 100 rotation in a minute(60 second)
So, in 30 seconds it will complete 50 rotation.
1 rotation = [tex] \frac{2200}{7} cm [/tex]
[tex] 50 rotation=\frac{2200}{7} \times 50cm \\\\ \frac{110000}{7} cm[/tex]
Break it in decimal.
Your answer will be 15714.2 cm
Lightning produces a maximum air temperature on the order of 104K, whereas a nuclear explosion produces a temperature on the order of 107K. Find the order of magnitude of the wavelength radiated with greatest intensity by each of these sources. Name the part of the EM spectrum where you would expect to radiate most strongly.
Answer:
tex]2.898\times 10^{-7}\ \text{m}[/tex] ultraviolet region
[tex]2.898\times 10^{-10}\ \text{m}[/tex] x-ray region
Explanation:
T = Temperature
b = Constant of proportionality = [tex]2.898\times 10^{-3}\ \text{m K}[/tex]
[tex]\lambda[/tex] = Wavelength
[tex]T=10^4\ \text{K}[/tex]
From Wein's law we have
[tex]\lambda=\dfrac{b}{T}\\\Rightarrow \lambda=\dfrac{2.898\times 10^{-3}}{10^4}\\\Rightarrow \lambda=2.898\times 10^{-7}\ \text{m}[/tex]
The wavelength of the radiation will be [tex]2.898\times 10^{-7}\ \text{m}[/tex] and it is in the ultraviolet region.
[tex]T=10^7\ \text{K}[/tex]
[tex]\lambda=\dfrac{2.898\times 10^{-3}}{10^7}\\\Rightarrow \lambda=2.898\times 10^{-10}\ \text{m}[/tex]
The wavelength of the radiation will be [tex]2.898\times 10^{-10}\ \text{m}[/tex] and it is in the x-ray region.
Scroll over the answer choices to see the images. Choose all of the true statements concerning the corresponding image
The picture depicts an electric motor which turns electrical energy into mechanical energy.
The picture depicts a generator which turns electrical energy into mechanical energy
A series circuit is a good example of an electromagnet
F more wite is wound around this iron mail, the strength of the electromagnetic is increased
This image devices that the direction of the magnetic field does not depend on the direction of the current
Flow of electron |
Answer:
Explanation:
I jus did it on usatestprep
A torque of 36.5 N · m is applied to an initially motionless wheel which rotates around a fixed axis. This torque is the result of a directed force combined with a friction force. As a result of the applied torque the angular speed of the wheel increases from 0 to 10.3 rad/s. After 6.10 s the directed force is removed, and the wheel comes to rest 60.6 s later.
(a) What is the wheel's moment of inertia (in kg m2)? kg m
(b) What is the magnitude of the torque caused by friction (in N m)? N m
(c) From the time the directed force is initially applied, how many revolutions does the wheel go through?
______ revolutions
Answer:
[tex]21.6\ \text{kg m}^2[/tex]
[tex]3.672\ \text{Nm}[/tex]
[tex]54.66\ \text{revolutions}[/tex]
Explanation:
[tex]\tau[/tex] = Torque = 36.5 Nm
[tex]\omega_i[/tex] = Initial angular velocity = 0
[tex]\omega_f[/tex] = Final angular velocity = 10.3 rad/s
t = Time = 6.1 s
I = Moment of inertia
From the kinematic equations of linear motion we have
[tex]\omega_f=\omega_i+\alpha_1 t\\\Rightarrow \alpha_1=\dfrac{\omega_f-\omega_i}{t}\\\Rightarrow \alpha_1=\dfrac{10.3-0}{6.1}\\\Rightarrow \alpha_1=1.69\ \text{rad/s}^2[/tex]
Torque is given by
[tex]\tau=I\alpha_1\\\Rightarrow I=\dfrac{\tau}{\alpha_1}\\\Rightarrow I=\dfrac{36.5}{1.69}\\\Rightarrow I=21.6\ \text{kg m}^2[/tex]
The wheel's moment of inertia is [tex]21.6\ \text{kg m}^2[/tex]
t = 60.6 s
[tex]\omega_i[/tex] = 10.3 rad/s
[tex]\omega_f[/tex] = 0
[tex]\alpha_2=\dfrac{0-10.3}{60.6}\\\Rightarrow \alpha_1=-0.17\ \text{rad/s}^2[/tex]
Frictional torque is given by
[tex]\tau_f=I\alpha_2\\\Rightarrow \tau_f=21.6\times -0.17\\\Rightarrow \tau=-3.672\ \text{Nm}[/tex]
The magnitude of the torque caused by friction is [tex]3.672\ \text{Nm}[/tex]
Speeding up
[tex]\theta_1=0\times t+\dfrac{1}{2}\times 1.69\times 6.1^2\\\Rightarrow \theta_1=31.44\ \text{rad}[/tex]
Slowing down
[tex]\theta_2=10.3\times 60.6+\dfrac{1}{2}\times (-0.17)\times 60.6^2\\\Rightarrow \theta_2=312.03\ \text{rad}[/tex]
Total number of revolutions
[tex]\theta=\theta_1+\theta_2\\\Rightarrow \theta=31.44+312.03=343.47\ \text{rad}[/tex]
[tex]\dfrac{343.47}{2\pi}=54.66\ \text{revolutions}[/tex]
The total number of revolutions the wheel goes through is [tex]54.66\ \text{revolutions}[/tex].
A fisherman notices that his boat is moving up and down periodically without any horizontal motion, owing to waves on the surface of the water. It takes a time of 3.00 s for the boat to travel from its highest point to its lowest, a total distance of 0.700 m . The fisherman sees that the wave crests are spaced a horizontal distance of 5.50 m apart.
Required:
a. How fast are the waves traveling?
b. What is the amplitude of each wave?
c. If the total vertical distance traveled by the boat were 0.500 , but the other data remained the same, how fast are the waves traveling ?
d. If the total vertical distance traveled by the boat were 0.500 , but the other data remained the same, what is the amplitude of each wave?
Answer:
a) v = 0.9167 m / s, b) A = 0.350 m, c) v = 0.9167 m / s, d) A = 0.250 m
Explanation:
a) to find the velocity of the wave let us use the relation
v = λ f
the wavelength is the length that is needed for a complete wave, in this case x = 5.50 m corresponds to a wavelength
λ = x
λ = x
the period is the time for the wave to repeat itself, in this case t = 3.00 s corresponds to half a period
T / 2 = t
T = 2t
period and frequency are related
f = 1 / T
f = 1 / 2t
we substitute
v = x / 2t
v = 5.50 / 2 3
v = 0.9167 m / s
b) the amplitude is the distance from a maximum to zero
2A = y
A = y / 2
A = 0.700 / 2
A = 0.350 m
c) The horizontal speed of the traveling wave (waves) is independent of the vertical oscillation of the particles, therefore the speed is the same
v = 0.9167 m / s
d) the amplitude is
A = 0.500 / 2
A = 0.250 m
A physicist at a respected research laboratory reports a startling new
discovery. Her conclusions are based on data from many trials. However,
other scientists are unable to reproduce the results of the experiment
Which statement tells why the original experiment might be faulty?
A. The conclusion are based on multiple trials
B. The results are announced to the public
C. Experimental results cannot be produced
D. The experiment does not include sophisticated equipment
A 1.1-kg object is suspended from a vertical spring whose spring constant is 120 N/m. (a) Find the amount by which the spring is stretched from its unstrained length. (b) The object is pulled straight down by an additional distance of 0.20 m and released from rest. Find the speed with which the object passes through its original position on the way up.
Answer:
e = 0.0898m
v = 2.07m/s
Explanation:
a) According to Hooke's law
F = ke
e is the extension
k is the spring constant
Since F = mg
mg = ke
e = mg/k
Substitute the given value
e = 1.1(9.8)/120
e = 10.78/120
e = 0.0898m
Hence it is stretched by 0.0898m from its unstrained length
2) Total Energy = PE+KE+Elastic potential
Total Energy = mgh +1/2mv²+1/2ke²
Substitute the given value
5.0= 1.1(9.8)(0.2)+1/2(1.1)v²+1/2(120)(0.0898)²
Solve for v
5.0 = 2.156+0.55v²+0.48338
5.0-2.156-0.48338= 0.55v²
2.36 =0.55v²
v² = 2.36/0.55
v² = 4.29
v ,= √4.29
v = 2.07m/s
Hence the required velocity is 9.28m/s
Does latitude has an effect on weight? PLEASE HELP!
Answer:
yes
it does you weigh less on the equator than at the North or South Pole, but the difference is small. Note that your body itself does not change. Rather it is the force of gravity and other forces that change as you approach the poles. These forces change right back when you return to your original latitude.
What does a step-up transformer do?
A. It steps up the energy.
B. It steps up the power.
C. It steps up the voltage.
D. It steps up the current.
A standard 1kilogram weight is a cylinder 50.5mm in height and 52.0mm in diameter. What is the density of the meterial?(kg/m^3)
Answer:
The correct answer is - 93.24×10^4 kg/m^3.
Explanation:
Given:
height of cylinder: 50.5 mm
diameter = 52.0
then radius will be diameter/2 = 52/2 = 26
Formula:
Density = mass/ volume
Volume = πr^2h
solution:
Now the volume of a cylinder is v = (22/7)×r^2×h
= 22/7×26×26×50.5
= 107261.59 mm^3
Now volume in cubic meter V =10.7261 ×10^(-5) m^3
So density d = m/V = 1/(10.7261 ×10^(-5))
Or d = 93.24×10^4 kg/m^3
1. Although mercury is a metal, it is a liquid at room temperature. Mercury melts at about -39°C. If
the temperature of a block of mercury starts at -54°C and increases by 22°C, does the mercury melt?
Explain your answer.
Answer:
I think so because if it starts at a low temperature for that material, it should melt when you bring it up to that temperature.
Answer: Mercury
Explanation: Mercury is kinda like the opposite of regular semi-liquid. For ice to melt you need Fahrenheit to melt ice into water while you need Celsius to melt mercury.
Two solenoids of equal length are each made of 2000 turns of copper wire per meter. Solenoid I has a 5.00 cm radius; solenoid II a 10.0 cm radius. When equal currents are present in the two solenoids, the ratio of the magnitude of the magnetic field BIalong the axis of solenoid I to the magnitude of the magnetic field BIIalong the axis of solenoid II, BI/BII, is
Answer:
BI/BII = 1
Explanation:
The magnetic field due to a solenoid is given by the following formula:
[tex]B = \mu nI\\[/tex]
where,
B = Magnetic Field due to solenoid
μ = permeability of free space
n = No. of turns per unit length
I = current passing through the solenoid
Now for the first solenoid:
[tex]B_1 = \mu n_1I_1 \\[/tex]
For the second solenoid:
[tex]B_2 = \mu n_2I_2\\[/tex]
Dividing both equations:
[tex]\frac{B_1}{B_2} = \frac{\mu n_1I_1}{\mu n_2I_2}\\[/tex]
here, no. of turns and the current passing through each solenoid is same:
n₁ = n₂ and I₁ = I₂
Therefore,
[tex]\frac{B_1}{B_2} = \frac{\mu nI}{\mu nI}\\[/tex]
BI/BII = 1
A rifle fires a pellet straight upward, because the pellet rests on a compressed spring that is released when the trigger is pulled. The spring has a negligible mass and is compressed by from its unstrained length. The pellet rises to a maximum height of 6.10 m above its position on the compressed spring. Ignoring air resistance, determine the spring constant.
This question is incomplete, the complete question is;
A rifle fires a 2.10 × 10⁻² kg pellet straight upward, because the pellet rests on a compressed spring that is released when the trigger is pulled. The spring has a negligible mass and is compressed by 9.10 × 10⁻² m from its unstrained length. The pellet rises to a maximum height of 6.10 m above its position on the compressed spring. Ignoring air resistance, determine the spring constant.
Answer:
the spring constant is 303.5 N/m
Explanation:
Given the data in the question;
There is a potential energy associated with the spring;
we know that potential energy = kinetic energy
mgh = [tex]\frac{1}{2}[/tex]kx²
where k is the spring constant and x is the compression
as the pallet is fired, the spring gives kinetic energy which is converted into gravitational potential energy
so
m = 2.10 × 10⁻²
g = 9.81 m/s²
h = 6.10 m
x = 9.10 × 10⁻² m
we substitute
mgh = [tex]\frac{1}{2}[/tex]kx²
2.10 × 10⁻² × 9.81 × 6.10 = [tex]\frac{1}{2}[/tex] × K × ( 9.10 × 10⁻² )²
1.256661 = 0.0041405 × K
K = 1.256661 / 0.0041405
K = 303.5 N/m
Therefore, the spring constant is 303.5 N/m